2020/06/30 by Rachel Baïle, R. Baïle, Jean–François Muzy +3 · 4 citations
Economics, Econometrics and Finance · Environmental Science · Mathematics · Physics and Astronomy · #Ecosystem dynamics and resilience #Financial Risk and Volatility Modeling #Fractal #Geometry #Land Use and Ecosystem Services #Mathematical analysis #Mathematics #Multifractal system #Physics #Point process #Poisson distribution #Scaling #Statistical physics #Statistics #physics.data-an #physics.soc-ph
paper · pdf · doi:10.1016/j.physa.2020.125697
published in Physica A Statistical Mechanics and its Applications 568, 125697 (Elsevier BV) · 41 pages, 14 figures
arxiv created 2020/11/22 · openalex publication_date 2020/12/25 · arxiv updated 2021/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a simple and wide class of multifractal spatial point patterns as Cox processes which intensity is multifractal, i.e., the class of Poisson processes with a stochastic intensity corresponding to a random multifractal measure. We then propose a maximum likelihood approach by means of a standard Expectation-Maximization procedure in order to estimate the distribution of these intensities at all scales. This provides, as validated on various numerical examples, a simple framework to estimate the scaling laws and therefore the multifractal properties for this class of spatial point processes. The wildfire distribution gathered in the Prométhée French Mediterranean wildfire database is investigated within this approach that notably allows us to compute the statistical moments associated with the spatial distribution of annual likelihood of fire event occurence. We show that for each order q, these moments display a well defined scaling behavior with a non-linear spectrum of scaling exponents ζq. From our study, it thus appears that the spatial distribution of the widlfire ignition annual risk can be described by a non-trivial, multifractal singularity spectrum and that this risk cannot be reduced to providing a number of events per km2. Our analysis is confirmed by a direct spatial correlation estimation of the intensity logarithms whose the peculiar slowly decreasing shape corresponds to the hallmark of multifractal cascades. The multifractal features appear to be constant over time and similar over the three regions that are studied.